In this work we consider the use of frequency hopping (FH) communications waveforms for TDE. Thus a high dynamic range narrow band receiver may be employed, subject to the complexity of FH acquisition. Adequate time-bandwidth product for TDE can be achieved by processing over multiple hops. We consider each hop to be a narrow band, flat fading channel that is independent from hop to hop. This introduces carrier phase uncertainty for each hop, and the SNR varies over hops as well. There may also be a small unknown carrier frequency offset per hop, and data symbols may be known (e.g., training in a preamble) or unknown (during communications). We consider the case of known carrier frequencies and known data symbols in this work, but the model is general and more complex cases may be studied in future work.